# Questions tagged [kolmogorov-smirnov]

The Kolmogorov-Smirnov test is a test for goodness of fit of data to a distribution. It is often used to test whether a variable is normally distributed.

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### Integral of Kolmogorov-Smirnov metrics?

I want to to calculate the area of the differences between the (red) null and (blue) empirical distributions of x, like in , the arrow is the KS metric, but is there a name for the areae between the ...
240 views

### How can I interpret the result of the 3D two-sample Kolmogorov-Smirnov test computed in R?

I would like to check if the two three-dimensional samples could come from the same distributions. In my data two dimensions are coordinates and third dimension is distances. In K-S test we have null ...
217 views

### Anderson-Darling test for any distribution with unknown parameters

I have been spending the last two days trying to construct a solid answer to the question: What is the distribution that best describes my sample? I did the following: Plot the histogram (nomalized ...
533 views

### Calculate representative value for data

Assume there are ten data with values $a_1$, $a_2$, ..., $a_{10}$ each with different non-symmetric errors. The problem confronting me in brief is, to combine the 10 results $a_{i}$ and their ...
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### Test for difference between 2 bounded, paired, and integer valued discrete distributions

I am comparing customer ratings at origination and at default. My data looks like this ...
20 views

### Normality Test in SPSS [duplicate]

I checked my data to know if they're normally distributed using SPSS. However, I saw that KS test and SW test gives different significance values. They give conflicting significance values, KS test ...
500 views

### How can I reject or confirm the null hypothesis without p-value?

I have two, large, two- or three-dimensional samples. I have used implementation of multidimensional Kolmogorov-Smirnov test in R (named Peacock.test) to compare these two samples and calculate test ...
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### Quantile Kolmogorov-Smirnov based on Koenker and Xiao (2004) for a QAR(1)

my goal is to investigate if a process has a unit root at different quantiles, hence, I use a QAR(1) model. I checked the PACF and only the first lag seems to be relevant. All my coding is done in R ...
72 views

### Why null hypothesis of a statistical test is always opposite to what one wants to prove [closed]

Why is it that the null hypothesis is typically the opposite of what one believes to be true?
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### Two sample Kolmogorov-Smirnov test

I have multiple sets of large (n,m>1500) experimental data and I am comparing 2 of the datasets at a time. I thought the two sample Kolomogrov-Smirnov test would be a good way to see if my datasets ...
221 views

### check implementation ks test for distribution with estimators fitted from same data

I've read that the KS-test is biased when the pdf parameters are estimated from the same data source. This post on Cross Validated lead me to the paper which has a workaround using synthetic datasets. ...
32 views

### Penalty for Kolmogorov–Smirnov statistic when using more number of parameters?

When I use R square (Coefficient of determination), it can be adjusted according to the number of parameter being examed, My question is when I using K-S statistic, is there similar way to ...
120 views

### Testing when the Null Hypothesis is that the distributions do differ. Application in the case of Kolmogorov-Smirnov test

My area of interest is Classification (Machine Learning). A Classifier will typically output a conditional probability distribution (P(Y=1|X) ) and the question may arise whether this predicted PDF ...
634 views

### Which statistical test should I use (comparing two cohorts)?

So I am doing some research in the field of Medical Physics, in particular radiation treatment with photons and protons. Now, I have two cases I am unsure about. 1) Here I have several patients. ...
63 views

### Kolmogorov-Smirnov test with PDFs instead of data points?

I don't have a background in statistics, so I don't know exactly how to phrase my question, and I am likely misusing some of the statistic lingo. I have a model which I am fitting to 30 sets of data,...
1k views

### Kolmogorov Smirnov Z vs Mann Whitney U small sample size n= 15?

I have a small sample size of 15. I want to see if there is a difference in the nutrient intakes between two independent variables, group 1 n = 11, group 2 n= 4. The data is not normally distributed. ...
67 views

### Compare two distributions for the same entities

I'd like to compare two distributions of measurements for the same entities, to determine the degree to which the two distributions measure the same underlying phenomenon. For example, I'd like to ...
1k views

### Can the Wilcoxon rank sum test give a different result to the Kolmogorov-Smirnov test result?

Let's say I have two data sets (in R, say); $x_1, x_2,..., x_n$ and $y_1, y_2,..., y_n$. The Wilcoxon rank sum test rejects, indicating that the "X" population distribution differs from that for "Y". ...
219 views

### Testing whether a process is Wiener process

Ideally I would like links to code implementations (eg. Matlab ) or book references, but I would appreciate suggestions on various methods. We start with sampled process $X_{t}$. A straightforward ...
246 views

### Observation Independence Assumption in KS-Test

I am having a distribution of time delta between temporally successive events. I found that these observations are dependent on neighbours with small lag (ACF and PACF show high significance), hence ...
583 views

### Two-sample test for discrete data

I want to validate that two samples of data with ties do not come from the same underlying distribution. The data itself describes the repair cost of cars and has a continuous value range. My solution ...
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### Different ways of writing the Kolmogorov-Smirnov test statistic

I have a question on the Kolmogorov-Smirnov test. This is what I know about the test. Consider the sequence of i.i.d. random variables $\{Z_i\}_{i=1}^n$ and let $\{z_i\}_{i=1}^n$ be one possible ...
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### Comparing estimated distributions

Consider the following: I have samples from two groups, and I want to answer the question are the BMIs for the two samples (say men and women) drawn from the same distribution? I do not want to ...
2k views

### Comparing normalized histograms - Kolmogorov-Smirnov tests and binning

I have a query about comparing binned data (and the theoretical validity of doing so) and would be very grateful if anyone can help. In one of our experiments, we're detecting the distribution of two ...
221 views

### What to conclude about the results if the p-value is same in 2 Kolmogorov-Smirnov tests?

I am comparing observed and simulated acceleration distributions. There are 3 data sets: 1) acco = observed accelerations 2) ...
317 views

### A basic question about the Kolmogorov—Smirnov test and the $p$-value

I have a pretty basic doubt about the KS test (two samples). From what I understand: We reject null hypothesis, under the confidence parameter $\alpha$, if the p-value (that is, the probability ...
2k views

### approach for comparing two groups of frequency distributions

I need to test if there is a difference in frequency distribution of a variable between two groups of subjects. Each subject is characterized by a list of values, from which a frequency distribution ...
5k views

### Is there a multivariate two-sample Kolmogorov-Smirnov test?

Is there a multivariate alternative to two-sample Kolmogorov-Smirnov test? What I mean is a test that can be used to check whenever two underlying multidimensional distributions differ.
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### Why is the Kolmogorov–Smirnov (KS) test more popular than the Overlapping Coefficient (OVL)?

The Overlapping Coefficient (OVL) measures the common area between two Probability Density Functions (see this question for more details). Intuitively, this seems like a good way to gauge the ...
726 views

### Does my data follow power law distribution? dummy approach in R

I am trying to test if my data fits the inverse power law distribution. Specifically, I am interested if my damaged area (Shape_Area) is somehow distance dependent? I tried to apply examples from ...
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### Test that training and test sets are sampled consistently

I'm exploring the Titanic dataset as my first experience of a Kaggle. Firstly, I want to test that the training and test sets were indeed sampled randomly from the population. For continuous ...
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### KS test for bimodal and unimodal distribution?

I am quite new to statistical tests and not sure how to exactly describe my question. I searched but could not find similar questions. Please do let me know if this is a redundant question. Thank you! ...
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### Interpretation of the test statistics of ks.test, ad.test, and wilcox.test

I am currently writing my Master's Thesis and I have a question in regards to the Kolmogorov-Smirnov test (ks.test in R), Anderson-Darling test (ad.test in R), and Wilcox/Mann-Whitney U test (wilcox....
193 views

### What is a proper test of significance for large distributions with long tails?

I want to see if two distributions I have are significantly different or not. They have long tails but their log-transforms are close to being normal. The number of samples is usually large, anything ...
53 views

### What are good ways to compare how “representative” a smaller sample is compared to a larger sample from which it was taken?

So basically, we have a sample of known data taken from a larger sample of known data. Is there a good way to measure how "representative" that data is, especially in distributional terms, compared to ...
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### How do I claim this set of data follows an exponential distribution?

I have a set of data that has following histogram: I would like to guess it follows an exponential distribution. So I did some goodness of fit using KS test with MATLAB like following: ...
196 views

### constants in scipy implementation of kolmogorov-smirnov two sample test

I am hoping some more enlightened statistician can help me to understand two constants used in the source of the scipy implementation of k-s 2 sample test. I already sent an e-mail to the dev group, ...
233 views

### Implementing Kolmogorov-Smirnov 2 sample test using numpy arrays

I am currently running some analysis on two data sets. One is a 'background-only' sample that is modeled as a decaying exponential and the other is a "signal" sample that features a single peak on top ...
I compared two sets of data using KS-test. First set is empirical data X1 and the second is expected data X2 which is randomly sampled, normally distributed with mean $\mu$ and std dev $\sigma$. The ...
Say I have some data $(x_{1},\ldots,x_{n})$ which I believe to be drawn from some distribution $\nu_{\theta}(x)$. I'm moderately familiar with estimation techniques for $\theta$ when I have some ...